Which equation represents an inverse variation?

You are buying plants and soil for your garden. The soil cost $4 per bag and the plants cost $10 each. You want to buy at least

bixtya [17]

Answer:

The system of linear inequalities to model the situation is written as:

x + y ≥ 5..... Equation 1

4x + 10y ≤ 100..... Equation 2

Step-by-step explanation:

Let

The number is soil = x

The number of plants = y

You are buying plants and soil for your garden.

You want to buy at least 5 plants

At least = greater than or equal to with the inequality sign(≥)

Hence:

x + y ≥ 5..... Equation 1

The soil cost $4 per bag and the plants cost $10 each and can spend no more than $100.

No more than means Less than or equal to with the inequality sign( ≤ )

Hence:

$4 × x +$10 × y ≤ $100

= 4x + 10y ≤ 100..... Equation 2

Therefore, the system of linear inequalities to model the situation is written as:

x + y ≥ 5..... Equation 1

4x + 10y ≤ 100..... Equation 2

5 0

3 years ago

Bone-shaped treats are 5 for $3.50 at Shelley's store and Sarah wants to buy 12. She set up and solved this proportion to find h

Molodets [167]

Answer:

Her error was multiplying numerator by numerator ( that is Quantity of Bone-shaped treats)

Step-by-step explanation:

Sarah's calculation

Let

x = cost of 12 Bone-shaped treats

Quantity of Bone-shaped treats : price

5 : 3.5 = 12 : x

(5/3.5) = (12/x)

Cross product

3.5x=60 (Here is her error)

x=17.14

Correct calculation

Quantity of Bone-shaped treats : price

5 : 3.5 = 12 : x

5 / 3.5 = 12 / x

Cross product

5 * x = 3.5 * 12

5x = 42

x = 42 / 5

= 8.4

x = $8.4

Her error was multiplying numerator by numerator ( that is Quantity of Bone-shaped treats)

Instead of multiplying Quantity of Bone-shaped treats by cost

7 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=27%3D%281%2F3%29x%2F2%5C%5C" id="TexFormula1" title="27=(1/3)x/2\\" alt="27=(1/3)x/2\\" align=

ICE Princess25 [194]

Answer:

x = 162

Step-by-step explanation:

The equation editor lets you properly write exponents, so we have to assume that your equation is supposed to be equivalent to ...

27 = x/6

27·6 = x = 162 . . . . multiply by 6

_____

On the off chance you intend ...

$27=\left(\dfrac{1}{3}\right)^{\dfrac{x}{2}}$

you can solve this by taking logarithms and dividing by the coefficient of x. Using base 3 for the logarithm may be easiest.

$\log_3{(27)}=\dfrac{x}{2}\log_3{(3^{-1})}\\\\3=-\dfrac{x}{2} \qquad\text{simplify}\\\\-6=x \qquad\text{multiply by -2}$

This version of the equation has solution x = -6.

4 0

3 years ago

Classify the number as rational or irrational.

erastova [34]

2.876 is rational. It can be expressed as 2876/1000.
-(sqrt(16)) is rational. It can be expressed as -4/1.
3pi is irrational. Pi cannot be expressed as a fraction.
23/40 is rational. It can be expressed as 23/40.

Have a nice day!

3 0

3 years ago

Read 2 more answers

In the right triangle ?ABC, leg AC=6 cm and leg BC=8 cm. Point M and N belong to AB so that AM:MN:NB=1:2.5:1.5. Find area of ?MN

Licemer1 [7]

Given : In Right triangle ABC, AC=6 cm, BC=8 cm.Point M and N belong to AB so that AM:MN:NB=1:2.5:1.5.

To find : Area (ΔMNC)

Solution: In Δ ABC, right angled at C,

AC= 6 cm, BC= 8 cm

Using pythagoras theorem

AB² =AC²+ BC²

=6²+8²

= 36 + 64

→AB² =100

→AB² =10²

→AB =10

Also, AM:MN:NB=1:2.5:1.5

Then AM, MN, NB are k, 2.5 k, 1.5 k.

→2.5 k + k+1.5 k= 10

→ 5 k =10

Dividing both sides by 2, we get

→ k =2

MN=2.5×2=5 cm, NB=1.5×2=3 cm, AM=2 cm

As Δ ACB and ΔMNC are similar by SAS.

So when triangles are similar , their sides are proportional and ratio of their areas is equal to square of their corresponding sides.

$\frac{Ar(ACB)}{Ar(MNC)}=[\frac{10}{5}]^{2}$

$\frac{Ar(ACB)}{Ar(MNC)}=4$

But Area (ΔACB)=1/2×6×8= 24 cm²[ACB is a right angled triangle]

$\frac{24}{Ar(MNC)}=4$

→ Area(ΔMNC)=24÷4

→Area(ΔMNC)=6 cm²

4 0

3 years ago